# zbMATH — the first resource for mathematics

Exotic multiplications on Morava K-theories and their liftings. (English) Zbl 0729.55001
Théorie de l’homotopie, Colloq. CNRS-NSF-SMF, Luminy/Fr. 1988, Astérisque 191, 35-43 (1990).
[For the entire collection see Zbl 0721.00021.]
Let $$v_ n^{-1}BP$$ denote the localization at $$v_ n$$ of the Brown- Peterson spectrum associated to the odd prime p. Let $${\mathcal M}\triangleleft v_ n^{-1}BP_*$$ be a maximal ideal containing the invariant prime ideal $$I_ n=(p,v_ 1,...,v_{n-1})$$. $${\mathcal M}$$ defines a ring spectrum K($${\mathcal M})$$. Now assume that K($${\mathcal M})_*\cong K(n)_*\cong {\mathbb{F}}_ p[v_ n,v_ n^{-1}]$$ and denote by $$v_ n^{-1}BP({\mathcal M})$$ the Artinian completion of $$v_ n^{- 1}BP$$ with respect to $${\mathcal M}$$. The author constructs a splitting of $$v_ n^{-1}BP({\mathcal M})$$ similar to that given in the paper reviewed below (see Zbl 0729.55002).
##### MSC:
 55N15 Topological $$K$$-theory